The equation below was solved incorrectly. Describe the error and solve it correctly

Question

4x-3(x-5)=x
4x-3x+15=x
x+15=x
15=2x
15/2=x

Question 5 options:

x = 15; When moving the x to the right side, they made it 2x when it should have been x

x = -15; When moving the x to the right side, they made it 2x when it should have been - x

No Solution; When moving the x to the right side, they made it 2x when it should have become 0

Infinite Solutions; When moving the x to the right side, they made it 2x when it should have become 0

Answer 1

Let's analyze the steps taken in the solution to identify the mistake and solve the equation correctly.

The original equation is:

\[ 4x - 3(x - 5) = x. \]

Step 1: Distributing the -3

When distributing -3 in the equation, we have:

\[ 4x - 3(x - 5) = 4x - 3x + 15 = x. \]

So we can rewrite the equation as:

\[ 4x - 3x + 15 = x. \]

Step 2: Combining like terms

Now, combining like terms gives us:

\[ x + 15 = x. \]

Step 3: Subtracting x from both sides

Subtracting \(x\) from both sides:

\[ x + 15 - x = x - x \] \[ 15 = 0. \]

This concludes that \(15 = 0\), which is a contradiction. Therefore, the equation has no solution.

Conclusion

The error in the original solution occurred when transitioning from \(x + 15 = x\) to \(15 = 2x\). The correct treatment should result in \(15 = 0\), which indicates that there is no solution.

The correct answer based on the options provided is:

No Solution; When moving the x to the right side, they made it 2x when it should have become 0.